# Single Variable Calculus

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## Description

For courses in Calculus for students in engineering, science, and math.

Built from the ground up to meet the needs of today's calculus students, Single Variable Calculus was the first text to pair a complete calculus syllabus with the best elements of reform-like extensive verbalization and strong geometric visualization. The Third Edition of this groundbreaking text has been crafted and honed, making it the text of choice for those seeking the best of both worlds. It offers an exciting choice of problem sets.

show more

Built from the ground up to meet the needs of today's calculus students, Single Variable Calculus was the first text to pair a complete calculus syllabus with the best elements of reform-like extensive verbalization and strong geometric visualization. The Third Edition of this groundbreaking text has been crafted and honed, making it the text of choice for those seeking the best of both worlds. It offers an exciting choice of problem sets.

show more

## Product details

- Paperback | 782 pages
- 217.9 x 277.4 x 25.7mm | 1,632.95g
- 01 Jul 2002
- Pearson Education (US)
- Pearson
- United States
- English
- 3rd edition
- 0130415502
- 9780130415509

## Table of contents

Preface.

1. Functions and Graphs.

Preliminaries. Lines in the Plane. Functions and Graphs. Inverse Functions; Inverse Trigonometric Functions. Guest Essay: Calculus Was Inevitable, John Troutman.

2. Limits and Continuity.

The Limit of a Function. Algebraic Computation of Limits. Continuity. Exponential and Logarithmic Functions.

3. Differentiation.

An Introduction to the Derivative: Tangents. Techniques of Differentiation. Derivatives of Trigonometric, Exponential, and Logarithmic Functions. Rates of Change: Modeling Rectilinear Motion. The Chain Rule. Implicit Differentiation. Related Rates and Applications. Linear Approximation and Differentials. Group Research Project: Chaos.

4. Additional Applications of the Derivative.

Extreme Values of a Continuous Function. The Mean Value Theorem. Using Derivatives to Sketch the Graph of a Function. Curve Sketching With Asymptotes: Limits Involving Infinity. L'Hoipital's Rule. Optimization in the Physical Sciences and Engineering. Optimization in Business, Economics, and the Life Sciences. Group Research Project: Wine Barrel Capacity.

5. Integration.

Antidifferentiation. Area as the Limit of a Sum. Riemann Sums and the Definite Integral. The Fundamental Theorems of Calculus. Integration by Substitution. Introduction to Differential Equations. The Mean Value Theorem for Integrals; Average Value. Numerical Integration: The Trapezoidal Rule and Simpson's Rule. An Alternative Approach: The Logarithm as an Integral. Guest Essay: Kinematics of Jogging, Ralph Boas.

6. Additional Applications of the Integral.

Area between Two Curves. Volume. Polar Forms and Area. Arc Length and Surface Area. Physical Applications: Work, Liquid Force, and Centroids. Applications to Business, Economics, and Life Sciences. Group Research Project: Houdini's Escape.

7. Methods of Integration.

Review of Substitution and Integration by Table. Integration by Parts. Trigonometric Methods. Method of Partial Fractions. Summary of Integration Techniques. First-Order Differential Equations. Improper Integrals. Hyperbolic and Inverse Hyperbolic Functions. Group Research Project: Buoy Design.

8. Infinite Series.

Sequences and Their Limits. Introduction to Infinite Series: Geometric Series. The Integral Test; p-Series. Comparison Tests. The Ratio Test and the Root Test. Alternating Series; Absolute and Conditional Convergence. Power Series. Taylor and Maclaurin Series. Group Research Project: Elastic Tightrope.

9. Vectors in the Plane and in Space.

Vectors in R2. Coordinates and Vectors in R3. The Dot Product. The Cross Product. Parametric Representation of Curves; Lines in R3. Planes in R3. Quadric Surfaces. Group Research Project: Star Trek.

10. Vector-Valued Functions.

Introduction to Vector Functions. Differentiation and Integration of Vector Functions. Modeling Ballistics and Planetary Motion. Unit Tangent and Principal Unit Normal Vectors; Curvature. Tangential and Normal Components of Acceleration. Guest Essay: The Stimulation of Science, Howard Eves.

11. Partial Differentiation.

Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes, Approximations, and Differentiability. Chain Rules. Directional Derivatives and the Gradient. Extrema of Functions of Two Variables. Group Research Project: Desertification.

12. Multiple Integration.

Double Integration over Rectangular Regions. Double Integration over Nonrectangular Regions. Double Integrals in Polar Coordinates. Surface Area. Triple Integrals. Mass, Moments, and Probability Density Functions. Cylindrical and Spherical Coordinates. Jacobians: Change of Variables. Group Research Project: Space-Capsule Design.

13. Vector Analysis.

Properties of a Vector Field: Divergence and Curl. Line Integrals. The Fundamental Theorem and Path Independence. Green's Theorem. Surface Integrals. Stokes' Theorem. The Divergence Theorem. Guest Essay: Continuous vs. Discrete Mathematics.

14. Introduction to Differential Equations.

First-Order Differential Equations. Second-Order Homogeneous Linear Differential Equations. Second-Order Nonhomogeneous Linear Differential Equations. Group Research Project: Save the Perch Project.

Appendices.

Introduction to the Theory of Limits. Selected Proofs. Significant Digits. Short Table of Integrals. Trigonometric Formulas. Answers to Selected Problems. Credits.

Index.

show more

1. Functions and Graphs.

Preliminaries. Lines in the Plane. Functions and Graphs. Inverse Functions; Inverse Trigonometric Functions. Guest Essay: Calculus Was Inevitable, John Troutman.

2. Limits and Continuity.

The Limit of a Function. Algebraic Computation of Limits. Continuity. Exponential and Logarithmic Functions.

3. Differentiation.

An Introduction to the Derivative: Tangents. Techniques of Differentiation. Derivatives of Trigonometric, Exponential, and Logarithmic Functions. Rates of Change: Modeling Rectilinear Motion. The Chain Rule. Implicit Differentiation. Related Rates and Applications. Linear Approximation and Differentials. Group Research Project: Chaos.

4. Additional Applications of the Derivative.

Extreme Values of a Continuous Function. The Mean Value Theorem. Using Derivatives to Sketch the Graph of a Function. Curve Sketching With Asymptotes: Limits Involving Infinity. L'Hoipital's Rule. Optimization in the Physical Sciences and Engineering. Optimization in Business, Economics, and the Life Sciences. Group Research Project: Wine Barrel Capacity.

5. Integration.

Antidifferentiation. Area as the Limit of a Sum. Riemann Sums and the Definite Integral. The Fundamental Theorems of Calculus. Integration by Substitution. Introduction to Differential Equations. The Mean Value Theorem for Integrals; Average Value. Numerical Integration: The Trapezoidal Rule and Simpson's Rule. An Alternative Approach: The Logarithm as an Integral. Guest Essay: Kinematics of Jogging, Ralph Boas.

6. Additional Applications of the Integral.

Area between Two Curves. Volume. Polar Forms and Area. Arc Length and Surface Area. Physical Applications: Work, Liquid Force, and Centroids. Applications to Business, Economics, and Life Sciences. Group Research Project: Houdini's Escape.

7. Methods of Integration.

Review of Substitution and Integration by Table. Integration by Parts. Trigonometric Methods. Method of Partial Fractions. Summary of Integration Techniques. First-Order Differential Equations. Improper Integrals. Hyperbolic and Inverse Hyperbolic Functions. Group Research Project: Buoy Design.

8. Infinite Series.

Sequences and Their Limits. Introduction to Infinite Series: Geometric Series. The Integral Test; p-Series. Comparison Tests. The Ratio Test and the Root Test. Alternating Series; Absolute and Conditional Convergence. Power Series. Taylor and Maclaurin Series. Group Research Project: Elastic Tightrope.

9. Vectors in the Plane and in Space.

Vectors in R2. Coordinates and Vectors in R3. The Dot Product. The Cross Product. Parametric Representation of Curves; Lines in R3. Planes in R3. Quadric Surfaces. Group Research Project: Star Trek.

10. Vector-Valued Functions.

Introduction to Vector Functions. Differentiation and Integration of Vector Functions. Modeling Ballistics and Planetary Motion. Unit Tangent and Principal Unit Normal Vectors; Curvature. Tangential and Normal Components of Acceleration. Guest Essay: The Stimulation of Science, Howard Eves.

11. Partial Differentiation.

Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes, Approximations, and Differentiability. Chain Rules. Directional Derivatives and the Gradient. Extrema of Functions of Two Variables. Group Research Project: Desertification.

12. Multiple Integration.

Double Integration over Rectangular Regions. Double Integration over Nonrectangular Regions. Double Integrals in Polar Coordinates. Surface Area. Triple Integrals. Mass, Moments, and Probability Density Functions. Cylindrical and Spherical Coordinates. Jacobians: Change of Variables. Group Research Project: Space-Capsule Design.

13. Vector Analysis.

Properties of a Vector Field: Divergence and Curl. Line Integrals. The Fundamental Theorem and Path Independence. Green's Theorem. Surface Integrals. Stokes' Theorem. The Divergence Theorem. Guest Essay: Continuous vs. Discrete Mathematics.

14. Introduction to Differential Equations.

First-Order Differential Equations. Second-Order Homogeneous Linear Differential Equations. Second-Order Nonhomogeneous Linear Differential Equations. Group Research Project: Save the Perch Project.

Appendices.

Introduction to the Theory of Limits. Selected Proofs. Significant Digits. Short Table of Integrals. Trigonometric Formulas. Answers to Selected Problems. Credits.

Index.

show more